Semirings: Algebraic Theory And Applications In Computer Science

An introduction to the algebraic theory of semirings, including a treatment of some applications in theoretical computer science. The focus is on the general concepts and statements of the algebraic theory of semirings and aspects of theory needed for the aforementioned applications.

---

This book provides an introduction to the algebraic theory of semirings and, in this context, to basic algebraic concepts as e.g. semigroups, lattices and rings. It includes an algebraic theory of infinite sums as well as a detailed treatment of several applications in theoretical computer science. Complete proofs, various examples and exercises (some of them with solutions) make the book suitable for self-study. On the other hand, a more experienced reader who looks for information about the most common concepts and results on semirings will find cross-references throughout the book, a comprehensive bibliography and various hints to it.